Layered piezoelectric structures with arbitrary acoustic termination impedances.

Multilayer piezoelectric transducers and resonators are widely used for generating propagating and standing acoustic waves as well as for sensor devices. More recently, layered piezoelectric structures based on thin film technology became increasingly important for electromechanical filters used in mobile phones. As a consequence, analytical mathematical modeling of such structures is of high interest. In this paper, a general rigorous transfer matrix description for one-dimensional (1D) layered structures consisting of piezoelectric, visco-elastic, and dielectric layers of arbitrary number is introduced to characterize the electrical and mechanical behavior of a general piezoelectric transducer or resonator with two electrodes and arbitrary acoustic termination impedances (Rig-1D-model). This model is the most general 1D analytical description of layered piezoelectric structures available and can be used for the characterization of various composite transducer and resonant sensor applications. Considered in detail are layered structures with the technically important cases of only one electromechanically coupled mode, and the structure at one or both outer surfaces is in contact with semi-infinite media. For such devices, it is shown how the frequency dependence of the total electrical admittance and spatial dependence of the displacements can be calculated.

Single half-wavelength ultrasonic particle filter: predictions of the transfer matrix multilayer resonator model and experimental filtration results.

The quantitative performance of a "single half-wavelength" acoustic resonator operated at frequencies around 3 MHz as a continuous flow microparticle filter has been investigated. Standing wave acoustic radiation pressure on suspended particles (5-microm latex) drives them towards the center of the half-wavelength separation channel. Clarified suspending phase from the region closest to the filter wall is drawn away through a downstream outlet. The filtration efficiency of the device was established from continuous turbidity measurements at the filter outlet. The frequency dependence of the acoustic energy density in the aqueous particle suspension layer of the filter system was obtained by application of the transfer matrix model [H. Nowotny and E. Benes, J. Acoust. Soc. Am. 82, 513-521 (1987)]. Both the measured clearances and the calculated energy density distributions showed a maximum at the fundamental of the piezoceramic transducer and a second, significantly larger, maximum at another system's resonance not coinciding with any of the transducer or empty chamber resonances. The calculated frequency of this principal energy density maximum was in excellent agreement with the optimal clearance frequency for the four tested channel widths. The high-resolution measurements of filter performance provide, for the first time, direct verification of the matrix model predictions of the frequency dependence of acoustic energy density in the water layer.